When a thin film is formed on a substrate, it is useful for controlling a film formation process to measure an optical constant of the formed thin film and a speed of film formation in-situ. That is, during the film formation and at that place, whether a thin film of a target material is formed can be determined based on the optical constant of the formed thin film, and whether a thin film having a target film thickness is formed can be determined based on the speed at which the thin film is formed. Here, the speed of the thin film formation is obtained by dividing the thickness of the formed thin film by a forming time of the thin film. The speed is expressed by using units in which the thickness is divided by time such as nanometer/minute and micron/hour. The speed at which the thin film is formed is referred to as a growth rate below.
As a method of uniformly forming the thin film over a wide area with good reproducibility, a method of forming a film in vapor phase (vapor phase growth method) such as metal organic chemical vapor deposition (MOCVD), molecular beam epitaxy (MBE), and sputtering methods have been well known. These methods are important as industrial thin film forming methods. As an in-situ observing method of the optical constant and the growth rate of the thin film formed by these vapor phase growth methods, a method of monitoring a temporal change of a reflectance of light beam is known. In this method, an object on which the thin film is formed is irradiated with light beam through an optical window provided in a wall surface of a thin film forming device, and a reflectance of light beam having a specific wavelength is measured during a film formation process. In a case where a surface of the substrate on which the thin film is formed is a mirror surface, an observed reflectance of the light beam emitted to the thin film periodically changes relative to the film thickness of the thin film by an interference effect between reflected light beam on the surface of the formed thin film and reflected light beam on an interface between the substrate and the thin film. The optical constant and the film thickness of the formed thin film can be calculated based on the period of the change of the reflectance relative to the film thickness, the minimum value and the maximum value of the reflectance, and the like, and the growth rate can be calculated based on a film forming time of the thin film (refer to JP 5050044 B).
A method of calculating the optical constant and the growth rate of the formed film based on film thickness dependency of the reflectance will be described below.
In a case where light beam vertically enters the substrate, when it is assumed that a reflectance of an electric field at the interface between air (refractive index=1) and the thin film (refractive index=n, absorption coefficient=0) formed on the substrate be r0, the value r0 is expressed by the following formula (1). Hereinafter, in the present embodiment, “air” may be read as “vacuum” or “gas”.r0=(1−n)/(1+n)  (1)
A reflectance r1 at the interface between the thin film and the substrate is expressed by the following formula (2) by using an absorption coefficient ks of the substrate and a refractive index ns of the substrate.r1=(n−iks−ns)/(n+iks+ns)  (2)
In the formula (2), the reference i is an imaginary unit.
Reflected light beam from the actual thin film includes all of the reflected light beam of the interface between air and the thin film and light beam which passes through the interface between air and the thin film, reciprocating between the interface of the thin film on the side of the substrate and the interface on the side of air for p times (p is an integer of equal to or more than one), and then, passing through the interface between the thin film and air and returning to the air side. Furthermore, since the phase changes when the light beam passes through the thin film, in consideration of the change of the phase, an electric field Er of the reflected light beam is expressed by the following formula (3).
                                                                        E                r                            =                            ⁢                                                                    E                    0                                    ⁢                                      r                    0                                                  +                                                                            E                      0                                        ⁡                                          (                                              1                        -                                                  r                          0                          2                                                                    )                                                        ⁢                                                            r                      1                                        ·                                          exp                      ⁡                                              (                                                  i                          ⁢                                                                                                          ⁢                          2                          ⁢                          φ                                                )                                                                              ⁢                                      {                                          1                      -                                                                        r                          1                                                ⁢                                                                              r                            0                                                    ·                                                      exp                            ⁡                                                          (                                                              i                                ⁢                                                                                                                                  ⁢                                2                                ⁢                                                                                                                                  ⁢                                φ                                                            )                                                                                                                          +                                                                                                                                                            ⁢                                                                    (                                                                  -                                                  r                          1                                                                    ⁢                                              r                        0                                                              )                                    ⁢                  2                  ⁢                                                                          ⁢                                      exp                    ⁡                                          (                                              i                        ⁢                                                                                                  ⁢                        4                        ⁢                                                                                                  ⁢                        φ                                            )                                                                      +                …                            }                                                                          =                            ⁢                                                                    E                    0                                    ⁢                                      r                    0                                                  +                                                                            E                      0                                        ⁡                                          (                                              1                        -                                                  r                          0                          2                                                                    )                                                        ⁢                                                            r                      1                                        ·                                                                  exp                        ⁡                                                  (                                                      i                            ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            φ                                                    )                                                                    /                                              {                                                  1                          +                                                                                    r                              1                                                        ⁢                                                                                          r                                0                                                            ·                                                              exp                                ⁡                                                                  (                                                                      i                                    ⁢                                                                                                                                                  ⁢                                    2                                    ⁢                                                                                                                                                  ⁢                                    φ                                                                    )                                                                                                                                                                    }                                                                                                                                                                    =                            ⁢                                                E                  0                                ⁢                                                      {                                                                  r                        0                                            +                                                                        r                          1                                                ·                                                  exp                          ⁡                                                      (                                                          i                              ⁢                                                                                                                          ⁢                              2                              ⁢                                                                                                                          ⁢                              φ                                                        )                                                                                                                }                                    /                                      {                                          1                      +                                                                        r                          1                                                ⁢                                                                              r                            0                                                    ·                                                      exp                            ⁡                                                          (                                                              i                                ⁢                                                                                                                                  ⁢                                2                                ⁢                                                                                                                                  ⁢                                φ                                                            )                                                                                                                                            }                                                                                                          (        3        )            
The reference E0 in the formula (3) is an electric field of the light beam emitted to the thin film. Therefore, an electric field reflectance r of the thin film is expressed by the following formula (4).r=Er/E0={r0+r1·exp(i2φ)}/{1+r1r0·exp(i2φ)}  (4)
Here, a phase difference (referred to as phase below) φ generated when the light beam reciprocates the inside of the thin film once is expressed by the following formula (5) by using a refractive index n of the thin film, a film thickness d of the thin film, and a wavelength λ of the light beam.φ=2πnd/λ  (5)
As indicated in the formula (5), the phase φ is proportional to the film thickness d and linearly increases as the film thickness d increases. A reflectance (energy reflectance) of the observed light beam is proportional to the square of the amplitude of the reflectance of the electric field. That is, the reflectance of the electric field and the energy reflectance become periodic functions of the film thickness. Conversely, if it is assumed that the film thickness of the thin film is proportional to the growth time, n, ns, ks, and the growth rate (d/time) used in the formula (4) can be obtained from the temporal change of the reflectance through the formulas (1) and (2).
The above example indicates a case where a single film is formed on the substrate. However, the similar method can be used in a case where a thin film is additionally formed after one or more layers of thin films have been formed on the substrate. That is, in a case where two or more thin films are formed on the substrate, the refractive index and the film thickness of a layer on the substrate side of the outermost layer cannot be determined based on only a film thickness dependency of the outermost layer of the reflectance. However, a plurality of layers including the substrate and except for the outermost layer is assumed as a substrate virtually having a refractive index ns′ and an absorption coefficient ks′, and the refractive index and the growth rate of the outermost layer can be determined based on the film thickness dependency of the outermost layer of the reflectance.
To obtain the optical constant and the growth rate of the thin film to be formed by measuring the above reflectance, it is necessary to have a thickness with which the period of the reflectance relative to the film thickness can be estimated. In a case where the film thickness is very thin, the change of the reflectance relative to the film thickness is only a very small part of the period change. Therefore, the film thickness with which the reflectance is periodically changed cannot be obtained. To accurately estimate the film thickness with which the reflectance is periodically changed, the film thickness with which the reflectance is changed at least about ¼ of one cycle is needed. The film thickness depends on the wavelength of the light beam used to measure the reflectance and the refractive index of the formed film thickness. When it is assumed that the wavelength and the refractive index be respectively 700 nm and 2, the film thickness is estimated to about 50 nm.
On the other hand, as a specific example of the formed thin film having a small thickness, a Multiple Quantum Well (MQW) structure used for an active layer of a blue light beam emitting diode can be exemplified. The MQW structure is a laminated structure of thin films of InGaN layers (quantum well layer, referred to as well layer below) and GaN layers (referred to as barrier layer below). In the structure, a plurality of InGaN layers and GaN layers having a thickness of about several nm is repeatedly laminated. The thickness of the single layer of the InGaN layers and the GaN layers is much thinner than the film thickness of 50 nm which can be estimated by the change of the reflectance. Regarding the single layer of the InGaN layers or the GaN layers, the film thickness and the optical constant cannot be obtained. In addition, a difference between thin film formation temperatures of the InGaN layer and the GaN layer is about several tens of degrees in general. Since the reflectance of the substrate on which the thin film is formed depends on the temperature, it is more difficult to perform analysis based on the reflectance in the structures such as the Multiple Quantum Well structure.
The present invention has been made in view of the above problems. A purpose of the present invention is to provide a vapor phase growth rate measuring apparatus, a vapor phase growth apparatus, and a growth rate detection method capable of easily and accurately detect a growth rate of a thin film on a substrate. Specifically, the inventor found out that some parameters used to calculate the reflectance depend on the temperature, and these parameters are taken as fitting parameters of the change of the reflectance according to the temperature change so that the growth rate and the refractive index can be obtained in the growth of the thin film laminated film such as the MQW layer with the temperature change.